Hi Saffyro. Re free-floating planets bumping into each other:
A few billion years from now, the Andromeda galaxy is expected to merge with the Milky Way. Each of them contains - at a minimum estimate - 100 billion stars. Yet simulations have shown that very few stars, possibly none, will collide; such is the immensity of the space between them. Our entire solar system, were it to be intact at that time, would be expected to remain intact, even though it might be ejected, as a whole, from the galaxy. That seems to suggest that perhaps collisions between free-floating planets might also be rare.
The nearest star (other than our sun) is about 4.4 light years. That is 41,598,721,804,147.2 km. Rounding that off we get about 41E9 km between us and the nearest star. Jupiter's size would round to 143E3 km. So roughly 3E5 Jupiters could fit in that distance.
Even better when you correct it Bill: 4.16E13 km, so about 3E8 (300,000,000) Jupiters. I'm not sure that it's easier to visualize, but if you scale down Jupiter to the size of tennis ball, then the nearest star would be as far away as the Moon